Determine the vertex of the function f(x) = 3(x − 2)2 + 1.

Answer:

x^2 / 25 + y^2 / 9 = 1

Step-by-step explanation:

The major axis is along the x axis and the minor axis is on the y axis.

Major axis = 2a =  5--5 =10 so a = 5 and a^2 = 25.

Similarly b^2 = 3^2 = 9.

Answer:

[tex]\frac{x^2}{25}+\frac{y^2}{9}=1[/tex]

Step-by-step explanation:

Equation of ellipse is of form [tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex] where [tex](a,0) , (-a,0)[/tex] are the x-intercepts and [tex](0,b) , (0,-b)[/tex] are the y-intercepts . If [tex]a > b[/tex] then it is a horizontal ellipse and if [tex]a < b[/tex] then it is a vertical ellipse .

For horizontal axis ,

Here, [tex](a,0) , (-a,0)[/tex] are known as the vertices of ellipse and [tex](0,b) , (0,-b)[/tex] are the co-vertices of ellipse .

Horizontal axis is known as the major axis and vertical axis is known as the minor axis .

Here, x-intercepts are [tex](5,0) , (-5,0)[/tex] , take a = 5

y-intercepts are [tex](0,3) , (0,-3)[/tex] , take b = 3

As [tex]a > b[/tex] , it is a horizontal ellipse .

On putting a = 5 and b = 3 , we get equation as

[tex]\frac{x^2}{5^2}+\frac{y^2}{3^2} =1\\ \frac{x^2}{25}+\frac{y^2}{9} =1[/tex]

Answer:

Degree is 2 so it is a quadratic.

The number of terms is 2 so it is a binomial.

It is a binomial quadratic.

Step-by-step explanation:

Let's find the degree of the polynomial first. I'm going to consider first the degrees of 5x^2 and 3.

The degree of the monomial 5x^2 is 2 because x is the only variable and it's exponent is 2.

The degree of the monomial 3 is 0 because there is no variable.

The degree of 5x^2+3 is therefore 2 because that is the highest degree of the monomials contained with in this polynomial 5x^2+3.

Degree 2 has a special name.

The special name for a degree 2 polynomial is quadratic.

Let's look at the number of terms in 5x^2+3.

Terms are separated by addition and subtraction symbols so there are two terms.

There is a special name for a two-termed polynomial, it is binomial.

So this is the following information I collected on our given polynomial:

Degree is 2 so it is a quadratic.

The number of terms is 2 so it is a binomial.

It is a binomial quadratic.

Answer:

1.6 m

Step-by-step explanation:

The side of the sign, the ground, and the wire form a right triangle where the wire is the hypotenuse.

The angle of depression plus the upper interior angle of the triangle add to 90 degrees. That means that the upper acute angle of the triangle measures 90 - 28 = 62 deg.

Call the upper acute angle of the triangle Angle A and the height of the sign h.

tan A = opp/adj

tan 62 = 3/h

h tan 62 = 3

h = 3/tan 62

h = 1.6

Answer: 1.6 m

Answer:

The tall of the sign board is 1.6 m.

Step-by-step explanation:

Let's draw a diagram to represents the given situation.

In the diagram, the base of the festival sign to the ground forms 90°. So it is right triangle.

The angle of depression is 28°. The angle of the upper interior angle = 90° - 28° = 62°.

Now we can use the trigonometric ration "tan = [tex]\frac{Oppsoite}{Adjacent}[/tex]" and the height of the sign board.

Let's take "h" be the height/tall of the sign board.

As you can see in the diagram, the opposite side = 3m

Now plug in the given values in the tan ratio, we get

tan 62° = [tex]\frac{3}{h}[/tex]

The value of tan 62° = 1.88

So, 1.88 =  [tex]\frac{3}{h}[/tex]

h =  [tex]\frac{3}{1.88}[/tex]

h = 1.595

We are asked to round of the nearest tenths place.

So, h = 1.6 m

Therefore, the tall of the sign board is 1.6 m.

Answer:

The top one

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x + 1 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex] and y- intercept c = + 1

Since m > 0 then graph slopes upwards from left to right

That indicates the top or bottom graphs

The bottom one has a y- intercept of c = - 1

While the top one has a y- intercept of c = + 1

Hence the top graph is the graph of y = [tex]\frac{1}{2}[/tex] x + 1

Hence, the graph of f(x) = 2x is A.

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

On plotting the graph of f(x) = [tex]\frac{1}{2}x + 1[/tex],

we observe that it is coincident to option A.

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Answer:

(2, -16).

Step-by-step explanation:

(x - 6)(x + 2)

Convert to vertex form:

Expanding the parentheses we have:

x^2 + 2x - 6x - 12

= x^2 - 4x - 12

Completing the square:

= (x - 2)^2 - 4 - 12

= (x - 2)^2 - 16

So the vertex is (2, -16),

Answer:

[tex]\large\boxed{4.\ V=\dfrac{33.64\pi x}{3}\approx35.21x}\\\boxed{5.\ V=21\ cm^3}[/tex]

Step-by-step explanation:

4.

The formula of a volume of a cone:

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

We have

[tex]2r=11.6\to r=5.8,\ H=x[/tex]

Substitute:

[tex]V=\dfrac{1}{3}\pi(5.8^2)x=\dfrac{1}{3}\pi(33.64)x=\dfrac{33.64\pi x}{3}[/tex]

[tex]\pi\approx3.14[/tex]

[tex]V\approx\dfrac{(33.64)(3.14)x}{3}\approx35.21x[/tex]

5.

The formula of a volume of a pyramid:

[tex]V=\dfrac{1}{3}BH[/tex]

B - base area

H - height

In the base we have the square. The formula of an area of a square with side s:

[tex]A=s^2[/tex]

We have

[tex]s=3cm,\ H=7\ cm[/tex]

[tex]B=3^2=9\ cm^2[/tex]

[tex]V=\dfrac{1}{3}(9)(7)=(3)(7)=21\ cm^3[/tex]

Answer:

b = 11.25m

Step-by-step explanation:

The base length of a parrellelogram with an area of 33.75 square meters and a height of 3 meters​ is 11.25 meters.

Answer:

11.25 m

Step-by-step explanation:

area of parallelogram = base  x height

so base = area/height

we substitute the values :

base = 33.75/3

        = 11.25

Answer:

That's 972 people in total.

Step-by-step explanation:

Here's how to solve this problem by setting up an equation with a single unknown.

Let the number of children that visited the zoo be [tex]x[/tex].

There are twice as many adults as children. So the number of adults will be [tex]2x[/tex].

Each child's ticket costs [tex]\$1.20[/tex]. The [tex]x[/tex] children will contribute a total of [tex]1.20 x[/tex] dollars to the total admission fee.

Each adult's ticket costs twice as much as a child's ticket. That's [tex]2\times \$1.20 = \$2.40[/tex]. The [tex]2x[/tex] adults will contribute a total of [tex]2.40\times 2x =4.80x[/tex] dollars to the total admission fee.

However,

[tex]\begin{aligned}&\text{Admission fee from children} \\+&\text{Admission fee from adults} \\ = &\text{Total Admission fee collected}\end{aligned}[/tex].

In other words,

[tex]1.20x + 4.80x = 1944[/tex].

[tex]6x = 1944[/tex].

[tex]\displaystyle x = \frac{1944}{6} = 324[/tex].

In other words, [tex]324[/tex] children visited the zoo. Twice as many adults visited the zoo. That's [tex]2x = 648[/tex] adults. [tex]324 + 648 = 972[/tex] people visited the zoo in total.

Answer:

by geometry rules

for a triangle

external angle of a triangle is equal to the sum of two internal angle of the triangle ( other than external adjacent angle)

m<1= sum of m<2 and m<3

m<1= m<1+<2

m<1 = 31+72

m<1= 103

hope you are clear now !

Answer:

The correct answer is last option.  103

Step-by-step explanation:

Points to remember

Sum of any two angles of a triangle is equal to the exterior angle of the third angle

To find the measure of <1

It is given that m<2 = 31° and m< 3 = 72°

From the figure we can see that <2 and <3 are two angles of a triangle. And <1 is the exterior angle of third angle of same triangle.

Therefore we can write,

m<2 + m<3 = m<1

m<1 = 31 + 72

  = 103°

Therefore the correct answer is last option.  103

Answer:

The independent variable is the time (variable x)

The dependent variable is the number of cars he washes (variable y)

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In this problem

The relationship between the number of cars he washes and the time it takes  him to wash those cars represent a a proportional variation

Let

y -----> the number of cars he washes

x -----> the time

The linear equation is [tex]y=kx[/tex]

The independent variable is the time x

The dependent variable is the number of cars he washes y

Answer:

-3

Step-by-step explanation:

a₁ = a₂/r = 3/(-1)=-3

a₉ = a₁ · r⁸ = -3 · (-1)⁸ = -3 · 1 = -3

Answer:

Ellen's money would have earned $25 more than her money at her account

Step-by-step explanation:

* Lets explain how to solve the problem

- The simple Interest Equation (Principal + Interest)  is:

  A = P(1 + rt)  , Where

# A = Total amount (principal + interest)

# P = Principal amount

# r = Rate of Interest per year in decimal r = R/100

# t = Time period involved in months or years

* Lets solve the problem

- Ellen deposited $2,500 into a savings account that earns 5% interest

 per year

- Her friend's bank offers a 6% annual interest rate

* Lets calculate her money after 1 year in each account

# Her account

∵ P = $2500

∵ r = 5/100 = 0.05

∵ t = 1

∵ A = P(1 + rt)

∴ A = 2500(1 + 0.05 × 1) = 2500 (1.05) = 2625

* Her money would be $2625 in one year

# Her friend's account

∵ P = $2500

∵ r = 6/100 = 0.06

∵ t = 1

∵ A = P(1 + rt)

∴ A = 2500(1 + 0.06 × 1) = 2500 (1.06) = 2650

* Her money would be $2650 in one year

∵ 2650 - 2625 = 25

∴ Ellen's money would have earned $25 more than her money at her

  account

Answer:

the answer is a

Step-by-step explanation:

y = -2x +1

y = x + 5

-2x+1=x+5

-3x = 4

x= -4/3

y = -1 1/3 + 5= 3 2/3

Answer:

C

Step-by-step explanation:

Given

x² = 7x - 3 ( subtract 7x - 3 from both sides )

x² - 7x + 3 = 0 ← in standard form

with a = 1, b = - 7, c = 3

Using the quadratic formula to solve for x

x = ( - (- 7) ± [tex]\sqrt{(-7)^2-(4(1)(3)}[/tex] ) / 2

  = ( 7 ± [tex]\sqrt{49-12}[/tex] ) / 2

  = [tex]\frac{7+/-\sqrt{37} }{2}[/tex] → C

Answer:

90

Step-by-step explanation:

Alright first step what is the degree measure of LN.

A full rotation is 360 degrees so LN=360-270=90.

So angle M is half the difference of the intercepted arcs:

[tex]\frac{1}{2}(270-90)=\frac{1}{2}(180)=90[/tex]

The measure of the vertex angle from the given geometry figure is 90 degrees

The given circle is made up of arc and angles. In order to determine the value of <M, we will use the theorem

"The half of the difference between the arc is equal to the angle at the vertex

1/2(270 - (360 - 270)) = <M
<M = 1/2 (270 -90)

<M = 1/2(180)

<M = 90degrees

Hence the measure of the vertex angle from the given geometry figure is 90 degrees

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The recursive formula for the sequence -16, -33, -50, -67, .... is  f(n) = f(n - 1) - 17, f(1) = -16

Finding the recursive formula for the sequence

From the question, we have the following parameters that can be used in our computation:

-16, -33, -50, -67, ....

In the above sequence, we can see that -17 is added to the previous term to get the new term

This means that

First term, a = -16

Common difference, d = -17

The recursive formula for the sequence is then represented as

f(n) = f(n - 1) - 17, f(1) = -16

Answer:

3,100 ft^2

Step-by-step explanation:

Answer:

3,100 ft^2

Step-by-step explanation:

Answer:

x = 230

Step-by-step explanation:

Given

[tex]\sqrt{x-5}[/tex] = 15 ( square both sides )

x - 5 = 15² = 225 ( add 5 to both sides )

x = 230

Answer:

D. (-7/2, 3/2)

Step-by-step explanation:

x = (-6+(-1))/2 = -7/2

y = (-2+5)/2 = 3/2

Answer:  D.

[tex](\dfrac{-7}{2},\ \dfrac{3}{2})[/tex]

Step-by-step explanation:

The coordinates of mid point (x,y) of a line joining points [tex](x_1 , y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by :-

[tex]x=\dfrac{x_1+x_2}{2},\ y=\dfrac{y_1+y_2}{2}[/tex]

From the given graph , we can see that the line is joining two points (-6,-2) and (-1,5) .

Then, the mid point of the line is given by :-

[tex]x=\dfrac{-6+(-1)}{2},\ y=\dfrac{-2+5}{2}[/tex]

[tex]x=\dfrac{-6-1}{2},\ y=\dfrac{5-2}{2}[/tex]

[tex]x=\dfrac{-7}{2},\ y=\dfrac{3}{2}[/tex]

Hence, the midpoint of the given segment = [tex](\dfrac{-7}{2},\ \dfrac{3}{2})[/tex]

For this case we have that by definition, the domain of a function is given by all the values for which the function is defined.

While the range of the function is the set of all the values that [tex]f (x)[/tex] takes.

We have the following function:

[tex]f (x) = 4x + 9[/tex]

We evaluate in the domain:

[tex]f (-4) = 4 (-4) + 9 = -16 + 9 = -7\\f (-2) = 4 (-2) + 9 = -8 + 9 = 1\\f (0) = 4 (0) + 9 = 0 + 9 = 9\\f (2) = 4 (2) + 9 = 8 + 9 = 17[/tex]

ANswer:

{-7,1,9,17}

first off, is noteworthy that on the denominators, 17 and 37 are prime numbers, so we can't quite factor them, and denominators of 15 and 22, have no common factors so the LCD of all denominators is simply their product, 15*22*37*17.

what we do is, turn all fractions with the same denominator, so they all represent the same division of the whole, and from there we can simply look at which numerator is larger or smaller to sort them.

we'll do so by using the LCD of all denominators, and dividing the LCD by each denominator, our quotient we'll use to multiply the fraction, let's do so

[tex]\bf \cfrac{7}{15} \qquad \cfrac{17}{22}\qquad \cfrac{22}{37} \qquad \cfrac{5}{17}~\hspace{5em} \stackrel{\textit{so the LCD for those denominators is}}{15\cdot 22\cdot 37\cdot 17\implies 207570} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{207570\div 15 ~=~ 13838}{\cfrac{7\cdot 13838}{15\cdot 13838}}\qquad \stackrel{207570\div 22 ~=~ 9435}{\cfrac{17\cdot 9435}{22\cdot 9435}}\qquad \stackrel{207570\div 37 ~=~ 5610}{\cfrac{22\cdot 5610}{37\cdot 5610}}\qquad \stackrel{207570\div 17 ~=~ 12210}{\cfrac{5\cdot 12210}{17\cdot 12210}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \cfrac{96866}{207570}\qquad \cfrac{160395}{207570}\qquad \cfrac{123420}{207570}\qquad \cfrac{61050}{207570} \\\\\\ \stackrel{\textit{and if we sort them from greatest to least}}{\cfrac{160395}{207570}\qquad \cfrac{123420}{207570}\qquad \cfrac{96866}{207570}\qquad\cfrac{61050}{207570}}[/tex]

Answer:

Yes

Both equilateral and equiangular triangles

Step-by-step explanation:

The AA (Angle-Angle) similarity states that if two pairs of corresponding angles are congruent, then the triangles are similar

In equilateral triangles, all angles are equal.The corresponding sides of two equilateral triangles are congruent thus they will be similar. An Equiangular triangle is also an equilateral triangle because its interior angles are the same and add up to 180°.

Both equilateral and equiangular triangles are similar by the Angle-Angle Similarity Postulate because they each have two congruent angles with any other triangle of the same type.

The Angle-Angle (AA) Similarity Postulate states that two triangles are similar if two angles of one triangle are congruent to two angles of the other triangle. Equilateral triangles are similar by AA postulate because all angles in any equilateral triangle measure 60 degrees, thus any two will be congruent with any two angles in another equilateral triangle. Equiangular triangles are also similar by the AA postulate, as all their corresponding angles are equal. Consequently, both equilateral and equiangular triangles are similar according to the AA Similarity Postulate.

Answer:

Median: 4.5

Mode: 4

Mean: 6.7

Step-by-step explanation:

First lets find the median, the number in the middle. To do this we need to put this data set in ascending order

1,4,4,4,4,5,7,8,15,15

The two numbers in the middle are 4 and 5. Now we must add these two numbers together and then divide by 2.

[tex]\frac{4+5}{2} =\frac{9}{2} =4.5[/tex]

Nexte lets find the mode, the number that occurs the most. 4 appears 4 times, which is the greatest amount.

Now lets find the mean. First we need to find the sum of these 10 numbers

[tex]1+4+4+4+4+5+7+8+15+15=67[/tex]

Next we have to divide by the number of data points, which is 10

[tex]\frac{67}{10} =6.7[/tex]

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x-2y=-26\\x-y=-2&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}x-2y=-26\\-x+y=2\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-y=-24\qquad\text{change the signs}\\.\qquad\qquad y=24\\\\\text{Put the value of y to the second equation:}\\\\x-24=-2\qquad\text{add 24 to both sides}\\x=22[/tex]

Answer:

(a) The two ordered pairs are (0 , 340) and (4 , 285)

(b) The slope is m = -55/4

The slope means the rate of decreases of the owl population was 55/4

per year (P decreased by 55/4 each year)

(c) The model equation is P = -55/4 t + 340

(d) The owl population in 2022 will be 216

(e)  At year 2038 will be no more owl in the park

Step-by-step explanation:

* Lets explain how to solve the problem

- The owl population in 2013 was measured to be 340

- In 2017 the owl population was measured again to be 285

- The owl population is P and the time is t where t measure the numbers

 of years since 2013

(a) Let t represented by the x-coordinates of the order pairs and P

   represented by the y-coordinates of the order pairs

∵ t is measured since 2013

∴ At 2013 ⇒ t = 0

∵ The population P in 2013 was 340

∴ The first order pair is (0 , 340)

∵ The time from 2013 to 2013 = 2017 - 2013 = 4 years

∴ At 2017 ⇒ t = 4

∵ The population at 2017 is 285

∴ The second order pair is (4 , 285)

* The two ordered pairs are (0 , 340) and (4 , 285)

(b) The slope of any lines whose endpoints are (x1 , y1) and (x2 , y2)

     is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

∵ (x1 , y1) is (0 , 340) and (x2 , y2) is (4 , 285)

∴ x1 = 0 , x2 = 4 and y1 = 340 , y2 = 285

∴ [tex]m = \frac{285-340}{4-0}=\frac{-55}{4}[/tex]

* The slope is m = -55/4

∵ The slope is negative value

∴ The relation is decreasing

* The slope means the rate of decreases of the owl population was

  55/4 per year (P decreased by 55/4 each year)

(c) The linear equation form is y = mx + c, where m is the slope and c is

    the value of y when x = 0

∵ The population is P and represented by y

∵ The time is t and represented by t

∴ P = mt + c , c is the initial amount of population

∵ m = -55/4

∵ The initial amount of the population is 340

∴ P = -55/4 t + 340

* The model equation is P = -55/4 t + 340

(d) Lets calculate the time from 2013 to 2022

∵ t = 2022 - 2013 = 9 years

∵ P = -55/4 t + 340

∴ P = -55/4 (9) + 340 = 216.25 ≅ 216

* The owl population in 2022 will be 216

(e) If the model is accurate , then the owl population be be zero after

    t years

∵ P = -55/4 t + 340

∵ P = 0

∴ 0 = -55/4 t + 340

- Add 55/4 t to both sides

∴ 55/4 t = 340

- Multiply both sides by 4

∴ 55 t = 1360

- Divide both sides by 55

∴ t = 24.7 ≅ 25 years

- To find the year add 25 years to 2013

∵ 2013 + 25 = 2038

* At year 2038 will be no more owl in the park

Answer:

The mean is equal to the median.

Step-by-step explanation:

Median is the middle value of a given data set. In a symmetric distribution, the data on the left side of the median is equal to the data on the right side of the median. Therefore, the mean of that data is equal to the median of the symmetric distribution.

Answer:

the mean is less than the explanation

Step-by-step explanation:

I just checked

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{The formula is:}\dfrac{\huge\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}[/tex]

[tex]\huge\text{y}_2\huge\text{ = -1}\\\\\huge\text{y}_1\huge\text{ = 2}[/tex]

[tex]\huge\text{x}_2\huge\text{ = -1}\\\\\huge\text{x}_1\huge\text{ = -3}[/tex]

[tex]\dfrac{-1 -2 }{-1 - (-3)}[/tex]

[tex]\huge\text{-1 - 2 = -3}[/tex]

[tex]\huge\text{-1 - (-3) = 2 }[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: }\dfrac{-3}{2}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

1/6 of a cup of milk. Or at least that's my answer.

Step-by-step explanation:

Okay, we need to find out 25% of 2/3.

25% of 2/3 is 1/6.

To find out how much milk Zeinab needs for 1/4 of the original recipe, multiply 2/3 of a cup by 1/4. The answer is 1/6 of a cup of milk.

Detailed Explanation:

To find out how much milk Zeinab needs, we need to calculate 1/4 of the original amount of milk. The original recipe requires 2/3 of a cup of milk.

Start with the original amount: 2/3 of a cup of milk.

Multiply this amount by 1/4 to find the reduced quantity:

Multiply the fractions: 2/3 * 1/4

Simplify the result, which is 1/6 of a cup of milk.

So, Zeinab needs 1/6 of a cup of milk to make 1/4 of the original recipe.

Hence  1/6 of a cup of milk is required

Answer:

In order:

2nd step

1st step

3rd step

4th step

Step-by-step explanation:

The checking part comes last.

Before you can determine the solution, your lines need to be graphed.

To graph your lines, they have to be in a form for you to determine how to graph them.

So the first step here is

"Write each equation in a form that is easy to graph"

The second step is:

To graph them

Third step is:

To see where they cross

The last step:

(Some people don't do it but should is check it).